Chapter 9: Elasticity and Fracture

1
Chapter 9 Elasticity and Fracture

• Christopher Chui

2
Statics Forces in Equilibrium

• 1st condition for equilibrium The sum of all
  forces is zero SFx 0, SFy 0, SFz 0
• 2nd condition for equilibrium The sum of all
  torques is zero St 0

3
Problem Solving in Statics

• Choose one body at a time for consideration, and
  make a careful free-body diagram to show all
  forces acting on it
• Choose a coordinate system and resolve the forces
  into their components
• Using letters to represent unknowns, write down
  the equation for SFx 0, SFy 0, SFz 0
• For St 0 equation, choose any axis
  perpendicular to the xy plane. Pay attention to
  the sign of the torque
• Solve these equations for the unknowns

4
Stability and Balance

• If an object is displaced slightly, 3 possible
  outcomes 1) the object returns to its original
  positionstable equilibrium 2) the object moves
  even fartherunstable equilibrium 3) the object
  remains in its new positionneutral equilibrium
• A body whose CG is above its base of support will
  be stable if a vertical line projected downward
  from the CG falls within the base of support

5
Elasticity, Stress and Strain

• Hookes law DL is proportional to applied force
• There is a limit of elasticity plasticity
  follows and finally breaking
• DL (1/E)(F/A)Lo E is elastic or Youngs modulus
• Stress force / area F/A
• Strain change in length / original length DL
  / Lo
• E stress / strain

6
Three Types of Stresses

• Tensile stress
• Compressive stress
• Shear stress
• Shear strain DL (1/G)(F/A) Lo where G is
  shear modulus ½ to 1/3 of the elastic modulus
• DV/Vo -(1/B) DP, where B is the bulk modulus